Search results
Results From The WOW.Com Content Network
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain.
Secret sharing consists of recovering a secret S from a set of shares, each containing partial information about the secret. The Chinese remainder theorem (CRT) states that for a given system of simultaneous congruence equations, the solution is unique in some Z/nZ, with n > 0 under some appropriate conditions on the congruences.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
By the Chinese remainder theorem, arithmetic modulo N corresponds to arithmetic in all the reduced groups simultaneously. The aim is to find an element which is not the identity of the group modulo N, but is the identity modulo one of the factors, so a method for recognising such one-sided identities is required. In general, one finds them by ...
The Zhoubi Suanjing contains an in-depth proof of the Gougu Theorem, a special case of the Pythagorean theorem) but focuses more on astronomical calculations. However, the recent archaeological discovery of the Tsinghua Bamboo Slips , dated c. 305 BCE , has revealed some aspects of pre-Qin mathematics, such as the first known decimal ...
The main theorem of strong approximation (Kneser 1966, p.188) states that a non-solvable linear algebraic group G over a global field k has strong approximation for the finite set S if and only if its radical N is unipotent, G/N is simply connected, and each almost simple component H of G/N has a non-compact component H s for some s in S ...
The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number.